Interaction of toroidal swimmers in Stokes flow

Jianjun Huang and Lisa Fauci
Phys. Rev. E 95, 043102 – Published 5 April 2017
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Abstract

A doughnut-shaped object supporting surface rotations was a hypothetical construct proposed by both Taylor and Purcell as a swimmer that would be able to propel itself in a Stokesian fluid because of the irreversibility of its stroke. Here we numerically examine the hydrodynamic interaction of pairs and trios of these free toroidal swimmers. First, we study the axisymmetric case of two toroidal swimmers placed in tandem, and show that a single torus of a corotating pair is more efficient than when it swims alone, but less efficient when paired with a counterrotating partner. Using a regularized Stokeslet framework, we study the nonaxisymmetric case of toroidal swimmers whose axes are initially parallel, but not collinear. These perturbed in tandem swimmers can exhibit qualitatively different trajectories that may, for instance, repel the swimmers or have them settle into a periodic state. We also illustrate interesting dynamics that occur for different initial configurations of three tori.

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  • Received 4 November 2016

DOI:https://doi.org/10.1103/PhysRevE.95.043102

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsPhysics of Living Systems

Authors & Affiliations

Jianjun Huang*

  • Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA

Lisa Fauci

  • Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA

  • *jhuang3@tulane.edu
  • fauci@tulane.edu

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Issue

Vol. 95, Iss. 4 — April 2017

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